Why does the mirror modifier disappear when I merge objects together?
When you merge two or more objects together, all selected objects will inherit the modifier stack of the active object (the object selected last).
If you're selecting the teeth object first (the object that has the Mirror modifier) then the key object (the active object that doesn't have it), the Mirror modifier will be deleted, since the active object doesn't have one.
The best solution is to copy the object that has the Mirror modifier, put it on a different layer for backup, then go to the original object and apply the Mirror modifier before merging it with the key object.